Dynamics of Visons and Thermal Hall effect in Perturbed Kitaev models

A vison is an excitation of the Kitaev spin liquid which carries a Z₂ gauge flux. While immobile in the pure Kitaev model, it becomes a dynamical degree of freedom in the presence of perturbations. We study an isolated vison in the isotropic Kitaev model perturbed by a small external magnetic field h, an off-diagonal exchange interaction Γ, and a Heisenberg coupling J. In the ferromagnetic Kitaev model, the dressed vison obtains a dispersion linear in Γ and h and a fully universal low-T mobility, μ=6?v²m/(k_BT)², where v_m is the velocity of Majorana fermions. In contrast, in the antiferromagnetic (AFM) Kitaev model interference effects suppress coherent propagation and an incoherent Majorana-assisted hopping leads to a T-independent mobility. The motion of a single vison due to Heisenberg interactions is strongly suppressed for both signs of the Kitaev coupling. Vison bands in AFM Kitaev models can be topological and may lead to characteristic features in the thermal Hall effects in Kitaev materials. Furthermore, we argue that vison diffusion leads to universal signatures in quench experiments.